Average Error: 0.0 → 0.0
Time: 18.2s
Precision: 64
\[\frac{-\left(f + n\right)}{f - n}\]
↓
\[\mathsf{log1p}\left(\mathsf{expm1}\left(\frac{-\left(f + n\right)}{f - n}\right)\right)\]
\frac{-\left(f + n\right)}{f - n}
↓
\mathsf{log1p}\left(\mathsf{expm1}\left(\frac{-\left(f + n\right)}{f - n}\right)\right)
double f(double f, double n) {
        double r29521 = f;
        double r29522 = n;
        double r29523 = r29521 + r29522;
        double r29524 = -r29523;
        double r29525 = r29521 - r29522;
        double r29526 = r29524 / r29525;
        return r29526;
}
↓
double f(double f, double n) {
        double r29527 = f;
        double r29528 = n;
        double r29529 = r29527 + r29528;
        double r29530 = -r29529;
        double r29531 = r29527 - r29528;
        double r29532 = r29530 / r29531;
        double r29533 = expm1(r29532);
        double r29534 = log1p(r29533);
        return r29534;
}

Error

Bits error versus f

Bits error versus n

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.0

    \[\frac{-\left(f + n\right)}{f - n}\]
  2. Using strategy rm

  3. Applied log1p-expm1-u0.0

    \[\leadsto \color{blue}{\mathsf{log1p}\left(\mathsf{expm1}\left(\frac{-\left(f + n\right)}{f - n}\right)\right)}\]

  4. Final simplification0.0

    \[\leadsto \mathsf{log1p}\left(\mathsf{expm1}\left(\frac{-\left(f + n\right)}{f - n}\right)\right)\]

Reproduce

herbie shell --seed 2019325 +o rules:numerics
(FPCore (f n)
  :name "subtraction fraction"
  :precision binary64
  (/ (- (+ f n)) (- f n)))